# Adiabatic process and the equation of state.

A sample of 8.02 x 10^-1 moles of nitrogen gas (gamma=1.40) occupies a volume of 2.00 x 10^-2 m^3 at a pressure of 1.00 x 10^5 Pa and temperature 300K. the sample is adiabatically compressed to half its original volume, nitrogen behaves as an ideal gas under these conditions. Show from the adiabatic condition and the equation of state that TVgamma-1 remains constant, and hence determine the final temperature of the gas? calculate the change in internal energy of the gas and the work done in compressing the gas?

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#### Solution Preview

Please see the attached file.

You can also use the "temodynamic calculator" found on:

http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/adiab.html#c1

In adiabatic conditions, Q=0 (there is no heat transfer from or to the system).

The first law of thermodynamics (conservation of energy) states that:

(1)

Where dU is the change of the internal energy of the system, which is the result of the difference between heat entering the system ( ) and work done by the system (dW). means that this is not full derivative, but rather an amount of ...

#### Solution Summary

The expert uses the first law of thermodynamics and the equation for adiabatic process, we can find value for several thermodynamical properties.